Proficiency in teaching mathematics is related to effectiveness: consistently helping students learn worthwhile mathematical content. It also entails versatility: being able to work effectively with a wide variety of students in different environments and across a range of mathematical content. Despite the common myth that teaching is little more than common sense or that some people are just born teachers, effective teaching practice can be learned. Just as mathematical proficiency itself involves interwoven strands, teaching for mathematical proficiency requires similarly interrelated components: conceptual understanding of the core knowledge of mathematics, students, and instructional practices needed for teaching; procedural fluency in carrying out basic instructional routines; strategic competence in planning effective instruction and solving problems that arise while teaching; adaptive reasoning in justifying and explaining one’s practices and in reflecting on those practices; and a productive disposition toward mathematics, teaching, learning, and the improvement of practice.
Effective programs of teacher preparation and professional development help teachers understand the mathematics they teach, how their students learn that mathematics, and how to facilitate that learning. In these programs, teachers are not given prescriptions for practice or readymade solutions to teaching problems. Instead, they adapt what they are learning to deal with problems that arise in their own teaching.
As a goal of instruction, mathematical proficiency provides a better way to think about mathematics learning than narrower views that leave out key features of what it means to know and be able to do mathematics. It takes time for proficiency to develop fully, but in every grade in school, students can demonstrate mathematical proficiency in some form. The overriding premise of our work is that throughout the grades from pre-K through 8 all students can and should be mathematically proficient.
The overriding premise of our work is that throughout the grades from pre-K through 8 all students can and should be mathematically proficient.
School mathematics in the United States does not now enable most students to develop the strands of mathematical proficiency in a sound fashion. Proficiency for all demands that fundamental changes be made concurrently in curriculum, instructional materials, assessments, classroom practice, teacher preparation, and professional development. These changes will require continuing, coordinated action on the part of policy makers, teacher educators,